Subgame-consistent cooperative solutions in randomly furcating stochastic differential games

The paradigm of randomly-furcating stochastic differential games incorporates additional stochastic elements via randomly branching payoffs in stochastic differential games. This paper considers dynamically stable cooperative solutions in randomly furcating stochastic differential games. Analytically tractable payoff distribution procedures contingent upon specific random realizations of the state and payoff structure are derived. This new approach widens the application of cooperative differential game theory to problems where the evolution of the state and future environments are not known with certainty. Important cases abound in regional economic cooperation, corporate joint ventures and environmental control. An illustration in cooperative resource extraction is presented.     

Subgame Consistent Cooperative Solutions in Stochastic Differential Games

Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that: (i) the extension of the solution policy to a later starting time and to any possible state brought about by the prior optimal behavior of the players would remain optimal; (ii) all players do not have incentive to deviate from the initial plan. In this paper, we develop a mechanism for the derivation of the payoff distribution procedures of subgame consistent solutions in stochastic differential games with transferable payoffs. The payoff distribution procedure of the subgame consistent solution can be identified analytically under different optimality principles. Demonstration of the use of the technique for specific optimality principles is shown with an explicitly solvable game. For the first time, analytically tractable solutions of cooperative stochastic differential games with subgame consistency are derived.     

A commuting-vector-field approach to some dispersive estimates

We prove the pointwise decay of solutions to three linear equations: (1) the transport equation in phase space generalizing the classical Vlasov equation, (2) the linear Schrödinger equation, (3) the Airy (linear KdV) equation. The usual proofs use explicit representation formulae, and either obtain \(L^1\)—\(L^\infty \) decay through directly estimating the fundamental solution in physical space or by studying oscillatory integrals coming from the representation in Fourier space. Our proof instead combines “vector field” commutators that capture the inherent symmetries of the relevant equations with conservation laws for mass and energy to get space–time weighted energy estimates. Combined with a simple version of Sobolev’s inequality this gives pointwise decay as desired. In the case of the Vlasov and Schrödinger equations, we can recover sharp pointwise decay; in the Schrödinger case we also show how to obtain local energy decay as well as Strichartz-type estimates. For the Airy equation we obtain a local energy decay that is almost sharp from the scaling point of view, but nonetheless misses the classical estimates by a gap. This work is inspired by the work of Klainerman on \(L^2\)—\(L^\infty \) decay of wave equations, as well as the recent work of Fajman, Joudioux, and Smulevici on decay of mass distributions for the relativistic Vlasov equation.     

The rotating bucket of sand: Experiment and theory

The surface shape of a bucket of sand rotating about its cylindrical axis is studied experimentally and theoretically. Focusing on fast time scales on which surface shape is determined by avalanches, we identify three regimes of behavior. At intermediate and high frequencies, the surface shape is always at its critical shape determined by the Coulomb yield condition. The low frequency behavior displays an unexpected subcritical region at the center of the bucket. To understand this central region, we adapt a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. The model indicates that the subcritical region is due to a nonlinear instability mechanism. (c) 1999 American Institute of Physics.     

Measurement of Titanium and Manganese K -shell Ionization Cross Sections by Electron Impact

报道了电子引起的钛、锰原子的Ｋ壳层电离截面实验值。实验中,采用了薄靶厚衬底技术,并将衬底中反射的电子对测量值的影响进行了修正。实验结果与其他文献报道的测量结果相吻合。最后,还将实验结果与Ｃａｓｎａｔｉ等人的经验公式进行了比较。     

Study of single cells by using capillary electrophoresis and native fluorescence detection

Capillary electrophoresis is known for its compatibility with biological materials and with small samples. It is an ideal tool for the study of single biological cells. Either whole cells or the material secreted from cells can be quantified. By continuously flowing a chemical stimulant over an immobilized cell inside the entrance of the capillary, one can even record the temporal progression of cellular secretion with sub-second resolution. The use of native fluorescence detection in such experiments provides a sensitive, rapid, non-intrusive and quantitative probe of important biomolecules such as catecholamines and proteins.     

Determination of adriamycin and daunorubicin in urine by high-performance liquid chromatography with laser fluorometric detection

A separation and detection scheme is presented for the determination of the antitumor drugs adriamycin and daunorubicin in human urine. Separation is accompished by reversed-phase high-performance liquid chromatography and the drugs are detected down to the low picograms level by laser excited fluoresence using a unique fiber optic based flow-cell. Excellent detector selectivity and linearity are reported, and some of the factors influencing the performance of the detector are discussed. Possible extension of the procedure to other biologically important determinations are mentioned.     

Structure selective complexation of cyclodextrins with five polyphenols investigated by capillary electrokinetic chromatography

The complexation of five polyphenols, namely trans‐resveratrol, astilbin, taxifolin, ferulic acid, and syringic acid (guest molecules) with α‐, β‐, and γ‐cyclodextrin (host molecules), was investigated by capillary electrokinetic chromatography. The binding constants were calculated based on the effective electrophoretic mobility change of guests with the addition of cyclodextrins into the background electrolyte. Because of cavity size, cyclodextrins showed structure‐selective complexation property to different guest. The stability of the trans‐resveratrol complexes was in the order of β‐ > α‐ > γ‐cyclodextrin. The cavity size of α‐cyclodextrin was too small for astilbin and taxifolin molecules, and thus they could not form complexes. The molecular size of syringic acid was too big for all cyclodextrins cavity, and no cyclodextrin could form complexes with it. Temperature studies showed that the binding constants decreased with the rise of temperature. Enthalpy and entropy values were calculated and the negative values of these parameters indicated that the complexation process was enthalpy‐controlled. Van der Waals force and release of high‐enthalpy water molecules from the cyclodextrins cavity played important roles in the process.